Accurate prediction method for a microstructure profile based on the force–displacement coupled servo model

Microstructures of specified shapes have been widely applied in electronics, communication, optics, avionics, medical science, and the automotive field. The ultraprecision single-point diamond turning lathe is a core instrument used in microstructure preparation. As a key technical indicator of an ultraprecision lathe, the servo control accuracy of a system directly affects the machining accuracy of the lathe. Because the profile error of microstructures machined by the slow tool servo of the ultraprecision lathe is at the micrometer level, any disturbance reduces the accuracy of parts machining. This paper proposes a tracking error prediction model based on the force–displacement coupled servo model to study the mechanism of action for the cutting force disturbance on a servo control system. The repeated positioning error of an ultraprecision lathe’s linear axis is added to the force–displacement coupled servo model to propose a more practical profile error prediction model and analyze the effect of the cutting force on the part profile. The experimental results indicate that the force–displacement coupled servo tracking error and profile error prediction model proposed in this paper is more accurate than the existing tracking error modeling method without cutting force disturbance. In addition, this paper analyzes how the cutting force in ultraprecision machining affects the servo system and part profile, which provides a reference for subsequent ultraprecision lathe error analysis and improved machining accuracy.